This proposal is concerned with the development of quantitative and theoretical models of the immune system. The last decade has seen explosive growth in detailed experimental findings about the cells, molecules and genes that make up the immune system. Before too long we will probably have almost complete information about the genes and possibly the molecules that influence the behavior of single lymphocytes. What will remain is the task of understanding how single cells interact with each other to generate the coordinate activity seen during and immune response. We propose to develop and analyze, using modern large scale computing techniques and state of the art analytical methods, an increasing realistic sequence of models of immune phenomena with the ultimate goal of understanding the operating principles of the immune system as a whole. There have been a number of initial modeling efforts in immunology. We propose to construct a new generation of models that aim to confront some of the complexities of the system. Our models will incorporate both idiotype network and clonal selectionist views. They will be novel and realistic in their inclusion of large numbers of lymphocyte clones, the control of cell growth and differentiation by various cytokines, and the explicit inclusion of B cells, T cells, and antigen presenting cells. The models will include considerable chemical detail of antigen-antibody and various receptor-ligand interactions. Among the general questions that we plan to explore are these: (I) What forces shaped the evolution of antibody V gene libraries? (II) How can one describe the antibody repertoire and the changes in the repertoire due to exposures to antigen? (III) What is the nature of memory in the immune system? (IV) What is the dynamics of affinity maturation? (V) How can one effectively describe the dynamics of an immune response with concurrent somatic mutation processes? (VI) Can we reconcile idiotype network and clonal selection views of the immune system? (VII) Is active suppression as opposed to lack of activation needed for efficient control of the immune system? If suppression is present, how specific is it compared to activation? (VIII) What is the trade-off between stability and controllability in the immune system? Specific health related issues include a proposed investigation of T cell vaccination for autoimmune disease and an inquiry into the spatial pattern of rashes. Most important is that progress in developing comprehensive models will provide a framework for viewing the algorithms underlying the operation of the immune system as a whole in fighting disease.